Investigation of the bond properties between hybrid fiber-reinforced concrete and BFRP bars after exposure to high temperature

2.1. Materials

P.O 42.5 normal Portland cement from Bohai Cement (Huludao) Co., Ltd. was used in this test. The local granite gravel was used as the coarse aggregate which had a continuous gradation in the 5-20 mm particle size range. The local ordinary river sand in Jinzhou was used as fine aggregate which had a fineness modulus of 2.7. Table 1 and Table 2 show the physical properties of coarse and fine aggregate, respectively. The granulometry curves of aggregates from the tests according to GB/T 14685-2022 (2828. GB/T 14685-2022. 2022. Pebble and crushed stone for construction. Chin. Stand.
) and GB/T 14684-2022 (2929. GB/T 14684-2022. 2022. Sand for construction. Chin. Stand.
) are shown in Figure 1. Urban tap water from Jinzhou City Tap Water Plant was used as the water. The BF and CF were from Jiangsu Tianlong Continuous Basalt Fibre Co., Ltd. and Taian Tongban FIBER Co., Ltd, respectively. The BFRP bars were 12 mm in diameter and 500 mm in length, with a sand-coated ribbed surface treatment, from Jiangsu Green Material Valley New Material Technology Development Co., Ltd. Table 3 and Table 4 show the material properties of fibers and BFRP bars, respectively. Figure 2 shows the appearance morphology of fibers and BFRP bars.

The concrete mixture proportion was designed according to JGJ 55-2011 (3030. JGJ 55–2011. 2011. Specification for Mix proportion design of ordinary concrete. Chin. Stand.
). The mix proportion of benchmark concrete was mass (cement): mass (sand): mass (coarse aggregate) = 1: 1.46: 2.06, and the water-binder ratio was 0.48. The volume content of BF and CF was set to be 0.15 % and 0.2 % of the concrete volume, respectively, based on existing research (3131. Zhu B. 2021. Experimental study on the bond behavior between BFRP bars and recycled aggregate concrete. Master thesis. Liaoning University of Technology.
, 3232. Xu H, Shao Z, Wang Z, Cai L, Li Z, Jin H, Chen T. 2020. Experimental study on mechanical properties of fiber reinforced concrete: Effect of cellulose fiber, polyvinyl alcohol fiber and polyolefin fiber. Constr. Build. Mater. 261:120610. https://doi.org/10.1016/j.conbuildmat.2020.120610
). The target temperature was set to be 20 °C, 100 °C, 200 °C, 300 °C, 400 °C and 500 °C. The main objective was to investigate the effect of the addition of BF and CF on the bond properties. Therefore, the change in fiber content was not considered.

2.2. Design of pull-out specimens

Table 5 shows the specimen groups. This test consisted of 8 groups of specimens, with 3 specimens in each group. The specimen number was represented by a combination of letters and numbers, where HN and HF respectively represented NC and HFRC, and the number represented the target temperature. For example, HF300 referred to specimens of HFRC after exposure to 300 °C.

The specimen with a 150 mm side length, following the guidelines of ACI440.3R-12 (3333. Committee ACI. 2012. ACI 440.3 R-12 Guide for test methods for fiber reinforced polymers (FRP) for reinforcing and strengthening concrete structures.
). The center of the cube specimen was vertically penetrated by the BFRP bar. Based on ACI 440.1R-06 (3434. Committee ACI. 2006. ACI 440.1 R-06 Guide for the design and construction of structural concrete reinforced with FRP bars.
) and the findings of Eduarda et al. (3535. Nepomuceno E, Sena-Cruz J, Correia L, D’Antino T. 2021. Review on the bond behavior and durability of FRP bars to concrete. Constr. Build. Mater. 287:123042. https://doi.org/10.1016/j.conbuildmat.2021.123042.
), the bond length was set to be 5d (60 mm), and the bond area was located in the upper portion of the concrete. The bond anchorage length was precisely controlled by sleeving a 90 mm ceramic sleeve in the unbonded area. The tape was used to attach the ceramic sleeve and the BFRP bar, and epoxy resin for 1 mm sealed both ends to avoid mortar intrusion during the casting process. The free end had a 20 mm length reserved for measuring the relative slip. The loading end was anchored by a galvanized steel tube with a 100 mm length to prevent its shear failure during the test. The specimens underwent curing at 23 ± 2 °C and 95 % humidity for 28 days after casting. Figure 3 shows the pull-out specimen.

2.3. Test setup

The SX2-12-10 box resistance furnace was used as the heating device, with a 10 °C/min heating rate and a 1200 °C maximum temperature. A high temperature protection treatment was applied to the exposed BFRP bars by wrapping them with a combination of fire retardant coating and fireproof asbestos before heating. After reaching the target temperature (100 °C, 200 °C, 300 °C, 400 °C, 500 °C), the specimens were maintained at constant temperature for 5h in the resistance furnace and then cooled to 20 °C. The temperature-time curves in the furnace were measured by the K-type thermocouple inside the resistance furnace, as shown in Figure 4. Before the formal test, conducted a pre-test to measure the temperature-time curve inside the specimen using a K-type thermocouple embedded in the BFRP bar bond area, as shown in Figure 5. After being held at a constant temperature for 5 hours, the internal temperature of each pull-out specimen reached the target temperature basically. At target temperatures of 100 °C, 200 °C, 300 °C, 400 °C, and 500 °C, respectively, HN specimens had an average heating rate of 0.36 °C/min, 0.62 °C/min, 0.95 °C/min, 1.35 °C/min, and 1.82 °C/min, the average heating rates of HF specimens were 0.35 °C/min, 0.60 °C/min, 0.94 °C/min, 1.39 °C/min, and 2.12 °C/min. The internal heating rate of the specimens increased as the target temperature increased, but it was lower than that of the high-temperature furnace. Furthermore, no concrete spalling occurred.

The central pull-out test was applied to the pull-out specimens in accordance with GB/T 30022-2013 (3636. GB/T 30022-2013. 2013. Test method for basic mechanical properties of fiber reinforced polymer bar. chin. stand.
). Before the test, the specimens should be placed in the reaction force test device which was shown in Figure 6(a). The device was primarily composed of two thick backing plates, a center retainer bar, and four long retainer bars. Adjusted the nuts of the four long retainer bars in the reaction force test device to make the bottom surface of the pull-out specimen tightly adhere to the steel plate to avoid eccentric loading. After adjusting the pull-out specimen, using the upper and lower fixtures of the WDW-300 KN electro-hydraulic servo testing machine to clamp the center retainer bar of the reaction force test device and the steel tube of the pull-out specimen respectively, as shown in Figure 6(b). A linear variable displacement transducer (LVDT) was placed between the free end and the end of the center retainer bar of the reaction force test device to measure the slip value. Afterward, it was loaded at a rate of 1 mm/min, which was controlled by displacement.

The average bond stress τ for each group of specimens was calculated according to ASTM D7913/D7913M-14 (3737. ASTM D7913/D7913M-14. 2014. Bond strength of fiber-reinforced polymer matrix composite bars to concrete by pullout testing. ASTM Stand.
). The formula is shown in Equation [1]:

Where τ was the average bond stress between the BFRP bar and concrete, MPa; P was the ultimate failure load of the specimen, N; d was the diameter of the BFRP bar, mm; l_a was the bond anchorage length of the BFRP bar, mm.

The TESCAN MIRA LMS and ZEISS Sigma 300 scanning electron microscopes were used to observe the internal microstructure of concrete. The SEM samples were taken from the concrete in the bonding interface.

3.1. Appearance morphology and tensile strength of bfrp bars after exposure to high temperatures

Figure 7 shows the appearance morphology changes of BFRP bars with the increase in temperature. Significant changes in surface color were caused by temperature increase. Before 200 °C, the surface color remained almost unchanged, and only a few sand particles fell off. The surface color turned to carbon black after 300 °C, and all the sand particles came off. The matrix resin of the BFRP bars began to decompose after reaching the melting point at 400 °C, and a golden brown color appeared. The fibers of the bars became loose after 500 °C, and the matrix resin completely decomposed and lost its viscosity. The severe decomposition of the matrix resin after 500 °C eliminated the tensile strength, which prevented the subsequent pull-out test from being conducted. Hence, the temperature range of the tensile test in this research was from 20 °C to 400 °C.

Table 6 shows the tensile test results. The BFRP bar had glass transition temperature (T_g) and thermal decomposition temperature (T_d) in a high-temperature environment (3838. Khaneghahi MH, Ghamsari AK, Ozbakkaloglu T. 2021. Stress-relaxation behavior of fiber-reinforced polymer sheets at elevated temperatures. Constr. Build. Mater. 307:124900. https://doi.org/10.1016/j.conbuildmat.2021.124900
). With rising temperatures, the tensile strength dropped. When exposed to 100 °C, the tensile strength was 1.6% lower than when it was at 20 °C. The tensile strength decreased by 6.3 % after exposure to 200 °C, where the BFRP bar matrix resin reached the T_g. The tensile strength partially recovered after the matrix resin solidified upon cooling to 20 °C. The tensile strength dropped by 41.8 % at 300 °C and reached only 13.2 % of its initial value at 400 °C. This was due to the resin matrix reaching the T_d at 300 °C and undergoing irreversible oxidation and decomposition after being heated at a constant temperature for 5h. The tensile strengths were not significantly influenced by temperatures below 300 °C compared to it at 20 °C. However, the tensile strength declined rapidly at 300 °C. The low resistance of FRP bars to high temperatures was mainly attributed to T_g and T_d of the resin. Only the specimens exposed to temperatures of 20 °C, 100 °C, 200 °C, and 300 °C conducted pull-out tests, as the tensile strength of the bar was severely deteriorated at 400 °C.

3.2. Microstructure of the concrete

Figures 8(a) and 8(b) show the SEM images of HF specimens at 20 °C. Figure 8(a) shows that the concrete mainly contained C-S-H gel, acicular ettringite (AFT), and hexagonal Ca(OH)₂ (CH). The microstructure was dense, and the pores were less. The aggregate and the solidified cementitious material were bonded together to form a uniform and dense continuous phase, which gave the cement paste a strong bond performance. Figure 8(b) shows that the surface of BF was covered by dense hydration products (C-S-H gel or CH crystal group). This indicated that there were good bonds in fiber and could be well embedded into the concrete matrix. This strong bond could enhance the force transfer of fiber, reduce internal damage, and then improve the bond properties. Figures 8(c) and 8(d) show that there were many voids in the HN specimen, and there was no substance inside the voids. However, the voids in the HF specimen were filled with a large amount of hydration products, which divided the large voids into small ones. The hydration products at the bonding interface in the HF specimen were significantly more than those in the HN specimen.

Figures 8(e) and 8(f) show the SEM images of HF and HN specimens at 200 °C, respectively. A lot of capillary water, free water, and bound water evaporated from the concrete at 200 °C, creating pores in the previously uniform and dense continuous medium. BF filled the pores and was slightly worn but not broken in HF, as shown in Figure 8(f). The gaps and micro-cracks in the concrete could be bridged. The secondary hydration reaction on the surface of BF produced many C-S-H gels and fine spherical particles that adhered to the fiber surface, which enhanced the mechanical interaction of fiber, and restrained the expansion of microcracks. The high thermal conductivity of BF could effectively transfer temperature and reduce the temperature gradient inside and outside the concrete.

Figure 8(g) ~ (h) show the SEM images of HF specimens after exposure to 300 °C. At 300 °C, the CF melted, and pores formed inside the matrix. Although the pores caused porosity to increase, they also provided a release channel for pore pressure and uneven thermal expansion stress. The decomposition of CH reduced the bond between cementitious materials and aggregates, resulting in a loose and porous internal structure of concrete. The surface of BF became smooth and had tiny cracks, indicating that the interface bonding force was weakened and some debonding occurred between fiber and matrix. Fiber fracture was the primary failure mode of BF, indicating that BF and matrix bear stress together before fracture. The cracks between BF and matrix further extended and connected with the pores left by the melting of CF to form the penetrating cracks.

3.3. Failure mode of pull-out specimens

Figure 9 illustrates the failure modes, which were classified as splitting failure, pull-out failure, and pull-out splitting failure.

In the case of splitting failure, a slight slip occurred on the loading end at the onset of the test loading, whereas the free end remained stable. As the load increased, the slip at the loading end increased, and the free end also began to slip. Splitting failure of the concrete occurred when the tangential tensile stress induced by the radial force exceeded the ultimate tensile strength of the concrete, resulting in an apparent brittle failure.

Pull-out failure specimens maintained good integrity, as no obvious cracks on the front and side. The bars were gradually pulled out with the increase in load, due to the shear strength of bars being much smaller than the tensile strength of concrete. When the free end was pulled out to a distance of roughly 20 mm, the loading was stopped. All specimens below 300 °C of HN and HF exhibited pull-out failures.

After 300 °C, the HN specimens experienced splitting failure, and the concrete was split into two pieces, whereas the HF specimens experienced pull-out splitting failure. The bars were gradually pulled out as the load increased, and obvious cracks emerged on the specimen surface in pull-out splitting failure, while integrity was preserved.

3.4. Bond strength

3.4.1. Influence of high temperature on bond strength

 ⌅

Table 7 presents the test results of the bond strength, and Figure 10 depicts the variation of bond strength with temperature. As the temperature rose, the bond strength of each group decreased. The bond strength of HN specimens reduced by 9.7 %, 18.0 %, and 27.3 %, respectively, after exposure to 100 °C, 200 °C, and 300 °C, compared with that of HN specimens at 20 °C. Similarly, the bond strength of HF specimens declined by 4.1 %, 11.7 %, and 20.8 %, respectively, compared with that of HF specimens at 20 °C.

TABLE 7.  Pull out test results of BFRP bar and hybrid fiber reinforced concrete.

Specimen number	F (kN)	τu (MPa)	Su (mm)	DR (%)	Failure mode
HN20	48.76	21.57	2.29	/	Pull out
HN100	44.01	19.47	3.10	9.74	Pull out
HN200	39.98	17.68	4.10	18.03	Pull out
HN300	35.45	15.68	5.10	27.31	Splitting
HF20	56.87	25.16	3.05	/	Pull out
HF100	54.55	24.13	3.25	4.09	Pull out
HF200	50.25	22.23	4.45	11.65	Pull out
HF300	45.05	19.93	6.35	20.79	Pull-out splitting

F: Ultimate load; τ_u: Bond strength; S_u: Peak slip value; DR: Decrease rate of bond strength.

FIGURE 10.  Bond strength.

For concrete, the free water and capillary water started to gradually evaporate and disappear at 100 °C, which made the porosity of the concrete increase (3939. Shen J, Xu Q. 2019. Effect of elevated temperatures on compressive strength of concrete. Constr. Build. Mater. 229:116846. https://doi.org/10.1016/j.conbuildmat.2019.116846
), resulting in a gradual decrease of concrete strength, which in turn, affected the bond strength negatively. At 200 °C, the proposition of free and capillary water evaporated increased, and the AFT dehydrated and decomposed, and degradation emerged on the interfacial transition zone (ITZ). At 300 °C, CH thermally decomposed into CaO, micro-cracks were generated by the thermal expansion of concrete, and the bond deterioration of the ITZ became more severe.

For BFRP bars, the tensile strength deteriorated with the temperature increase, and the deterioration was the most serious at 300 °C. Moreover, the thermal expansion coefficient between bars and concrete was different, tensile stress was generated inside the concrete when the temperature increased, which caused the generation of microcracks. Thus the bond property was influenced (4040. Bilotta A, Compagnone A, Esposito L, Nigro E. 2020. Structural behaviour of FRP reinforced concrete slabs in fire. Eng. Struct. 221:111058. https://doi.org/10.1016/j.engstruct.2020.111058.
). Furthermore, the sand particles on the bars’ surface fell off with the increase in temperature, and the ribs degraded and became shallow. The mechanical interaction and friction force that provided the bond stress were reduced to different degrees (4141. Katz A, Berman N, Bank LC. 1999. Effect of high temperature on bond strength of FRP rebars. J. Compos. Constr. 3(2):73-81. https://doi.org/10.1061/(ASCE)1090-0268(1999)3:2(73).
). The combined deterioration of concrete and BFRP bars made the bond strength decrease with the increased temperature, and the decrease became more pronounced.

3.4.3. Residual bond strength

 ⌅

The incorporation of BF and CF effectively increased the residual bond strength. The test data were used to establish the fitting curves of residual bond strength of HN and HF specimens, as shown in Figure 11. The fitting relationships were given by Equations [2] and [3].

FIGURE 11.  Fitting curves of residual bond strength of HN and HF specimens. (a) HN; (b) HF.

$\mathrm{H}\mathrm{N}:\frac{{\tau }^T}{{\tau }^{20}}=0.99895-9.405\times 10^{-4}T+1.25\times 10^{-7}{T}^2\mathrm{ }{R}^2=0.998$  [2]

$\mathrm{H}\mathrm{F}:\frac{{\tau }^T}{{\tau }^{20}}=1.00075-3.525\times 10^{-4}T-1.175\times 10^{-6}{T}^2\mathrm{ }{R}^2=0.999$  [3]

Where τ²⁰ was the bond strength of specimens after exposure to 20 °C, MPa; τ^T was the bond strength of specimens after exposure to high temperature, MPa; T was temperature, °C.

3.5. Bond-slip curve

Figure 12 shows the bond-slip curves. The change rule of the HN and HF specimens was consistent. The bond stiffness and bond strength of each specimen gradually decreased, and the peak slip increased, with the increase in temperature. Four stages could be divided into the curves: the micro slip stage, the slip stage, the pull-out stage, and the residual stress stage. However, there were only the first three stages on the curve of the splitting failure specimen (HF300). In the beginning, the curve was in the micro slip stage. There were micro slip occurrences on the loading end, and the bond stress increased linearly. The chemical adhesion mainly provided the bond stress. The curve entered the slip stage with the loading continued, where the relative slip began to appear, and the bond stress rose nonlinearly. The chemical adhesive force disappeared, and the mechanical interaction and friction force between the transverse rib of the BFRP bar and the concrete interface mainly provided the bonding force. After the bond stress reached peak value, the curve entered the pull-out stage. Due to the further wear of the ribs of the bars, the concrete between the ribs being cut into pieces, the mechanical interaction weakened sharply, resulting in a gradual decrease in the bond stress. A nonlinear decrease was shown in the bond stress in the residual stress stage. Due to the slow pull-out of BFRP bars, the free end reserved outside entered into the concrete, and the mechanical interaction and friction force between the transverse ribs on the free end and the concrete interface was generated, which made the specimen regain some bonding force.

3.5.1. Influence of high temperature on bond properties

 ⌅

The bond stiffness also decreased as temperature increased. The bond stiffness of HN decreased by 30.4 %, 53.2 %, and 67.5 % at 100 °C, 200 °C, and 300 °C, respectively, while the bond stiffness of HF decreased by 26.9 %, 52.7 %, and 55.0 % at the same temperatures. Figure 13 depicts the variation of bond stiffness with temperature.

FIGURE 13.  Bond stiffness.

The main reason for the above results was that the gradual vitrification, decomposition, and carbonization of matrix resin of BFRP bars with increased temperature, resulting in the gradual decrease of chemical adhesive force, friction force, and mechanical interaction force (4646. Alsayed S, Al-Salloum Y, Almusallam T, El-Gamal S, Aqel M. 2012. Performance of glass fiber reinforced polymer bars under elevated temperatures. Composites Part B. 43(5):2265-2271. https://doi.org/10.1016/j.compositesb.2012.01.034
). The specimens after exposure to 200 °C could restore the tensile strength of bars and the bond strength to a certain extent after they were naturally cooled to 20 °C. The polymer resin decomposed after 300 °C, and the tensile strength of the bars decreased significantly, which could not be restored. Hence, high temperature influenced the bond stiffness. Moreover, the extrusion between the transverse rib of the BFRP bar and the concrete produced the oblique force, which produced radial and tangential components and caused the surrounding concrete to be in a circumferential tension state. The bond failure would occur when the circumferential stress exceeded the concrete tensile strength. The temperature increase reduced the concrete tensile strength, which led to premature bond failure, and the bond strength and stiffness also reduced.

3.6. Bond-slip constitutive model between bfrp bar and concrete after exposure to high temperature

3.6.1. Existing models

 ⌅

Bond properties were the basis of the FRP bars and concrete working together. A lot of research on the bond properties has been done by scholars, and corresponding bond-slip constitutive models have been proposed. The function expressions of each model are shown in Table 8.

Table 8.  Bond-slip constitutive models.

Constitutive model	Function expressions
Malvar model	${\tau }_1/f_t=A+B\left(1-e^{C{\sigma }_r/f_t}\right);s_1=D+E{\sigma }_r;$ $\tau /{\tau }_1=\frac{F\left(s/s_1\right)+\left(G-1\right){\left(s/s_1\right)}^2}{1+\left(F-2\right)\left(s/s_1\right)+\left(G-1\right)\left(s/s_1\right)}$
BPE model	$\tau /{\tau }_1={\left(s/s_1\right)}^{\alpha },\left(s\le s_1\right)$ $\tau ={\tau }_1,(s_1<s\le s_2)$ $\tau ={\tau }_1-\frac{{\tau }_1-{\tau }_3}{s_2-s_3}\left(s_2-s\right),(s_2<s\le s_3)$ $\tau ={\tau }_3\left(s>s_3\right)$
MBPE model	$\tau /{\tau }_1={\left(s/s_1\right)}^{\alpha },\left(s\le s_1\right);$ $\tau =\left[1-p\left(s/s_1-1\right)\right]{\tau }_1,\left(s_1<s\le s_3\right);$ $\tau ={\tau }_3,(s>s_3)$
CMR model	$\tau ={\left(1-e^{-s/s_r}\right)}^{\beta }{\tau }_1$
Continuous curve model	$\tau =\left(2\sqrt{s/s_1}-\frac{s}{s_1}\right){\tau }_1,\left(0<s\le s_1\right);$ $\tau =\frac{{\tau }_1{\left(s_3-s\right)}^2\left(2s+s_3-s_1\right)}{{\left(s_3-s_1\right)}^3}+\frac{{\tau }_3{\left(s-s_1\right)}^2\left(3s_3-2s-s_1\right)}{{\left(s_3-s_1\right)}^3},\left(s_1<s\le s_3\right);$ $\tau ={\tau }_3,(s>s_3)$

σ_r: Axisymmetrical radial pressure; f_t: Tensile strength of concrete; τ₁ , s₁: Bond strength and peak slip; τ₃ , s₃: Residual strength and corresponding slip; A, B, C, D, E, F, G, α, β, s₂, s_r: Parameters determined by test results.

One of them was the Malvar model, which was proposed in 1994 by Malvar (4747. Malvar, L. J. 1994. Bond stress-slip characteristics of FRP rebars. Port Hueneme, CA, USA: Naval Facilities Engineering Service Center.
) after studying the influences of three different GFRP bars on bond strength. The axisymmetrical radial pressure σ_r was introduced, and the peak bond strength τ₁ and the peak slip s₁ defined the functional expression of σ_r . A subsequent model was the BPE model, which was proposed by Eligehausen et al. (4848. Eligehausen R, Popov EP, Bertero VV. 1982. Local bond stress slip relationship of deformed bars under generalized excitations. Calif. The Univ.
) in 1983 to describe the bond-slip curve of deformed steel bars. The BPE model was successfully applied by Cosenza et al. (4949. Cosenza E, Manfredi G, Realfonzo R. 1995. 20 Analytical modelling of bond between frp reinforcing bars and concrete. In Non-metallic (FRP) reinforcement for concrete structures: proceedings of the second international RILEM symposium. 29:164. CRC Press.
) to the analysis of FRP bars reinforced concrete structures. In this model, the curve was divided into 4 stages: an ascending stage, a horizontal stage, a descending stage, and a residual stage, as shown in Figure 14. Since there was no horizontal stage in practical engineering, in 1996, Cosenza et al. (5050. Cosenza E, Manfredi G, Realfonzo R. 1996. Bond characteristics and anchorage length of FRP rebars. Adv. Compos. Mater. Bridges Struct. 909-916.
) considered the actual situation. They improved the horizontal stage in the BPE model, namely the MBPE model, which is shown in Figure 15. Furthermore, it has been discovered that only the rising section of the curve needs to be considered in most structural calculations. Thus Cosenza et al. (5151. Cosenza E, Manfredi G, Realfonzo R. 1997. Behavior and modeling of bond of FRP rebars to concrete. J. Compos. Constr. 1(2):40-51. https://doi.org/10.1061/(ASCE)1090-0268(1997)1:2(40).
) proposed CMR model that could describe the rising section more accurately. For the purpose of making the bond-slip curve smoother and more continuous, Gao et al. (5252. Gao D, Zhu H, Xie J. 2003. The constitutive models for bond slip relation between FRP rebars and concrete. Ind. Constr. 07:41-43+82.
) introduced four parameters to modify the existing model and proposed a mathematical model of a constant curve.

FIGURE 14.  BPE model.

FIGURE 15.  MBPE model.

3.6.2. Bond-slip constitutive models comparison

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To achieve a more scientific and standardized application of FRP bar hybrid fiber reinforced concrete structure, using the Malvar, MBPE, CMR, and Continuous Curve models to fit ascending sections of bond-slip curves obtained from this test through Origin software, and the results were compared to verify the models. The comparison of the average coefficient of determination (average R² values) of each model obtained by fitting is shown in Figure 16. The average R² values of the Malvar, MBPE, CMR, and Continuous Curve models obtained by fitting were 0.997, 0.933, 0.988, and 0.775, respectively. It could be seen that the Malvar, CMR, and MBPE models could all fit the ascending sections of the curves accurately. The fitting effect of the Malvar model was the best, and the fitting effect of the CMR model was very close to the Malvar model, but slightly worse than the Malvar model. Although the MBPE model was worse than the Malvar model and CMR model, the R² values obtained by fitting the curves of each specimen were all above 0.9, which there was still a good fitting effect. The Continuous Curve model was the worst. Figures 17 and 18 show that the fluctuation of the fitting effect of each model on the ascending sections of HF was larger than that of HN. There was the same variation trend on the fitting effect of each model on HF as that of HN with the temperature increased from 20 °C to 200 °C.

FIGURE 16.  Comparison of R² values on ascending section.

FIGURE 17.  (a) R² values for the Malvar model fitting the ascending section; (b) R² values for the MBPE model fitting the ascending section; (c) R² values for the CMR model fitting the ascending section; (d) R² values for the Continuous Curve model fitting the ascending section.

FIGURE 18.  Comparison of curves of each model fitting ascending section. (a) HN100; (b) HN300; (c) HF100; (d) HF300.

Regarding the descending sections, using the Malvar, MBPE, and Continuous Curve models to fit them. The comparison of the fitting effects of each model is shown in Figure 19. The average R² values obtained from the Malvar, MBPE, and Continuous Curve models fitting the descending sections of the test curves for each specimen were 0.912, 0.952, and 0.978, respectively. The situation was different from that of fitting the ascending section, the Continuous Curve model was the best when fitting the descending section, and the MBPE model was slightly worse. The Malvar model was the worst, and it fluctuated significantly. It did not show the same good effect as that of fitting the ascending sections. Figure 20 and Figure 21 show that the fitting effects of each model on the descending sections of HN were better than that of HF. Similarly, there was still the same variation trend on the fitting effect of the Malvar model and Continuous Curve model on HF as that of HN with the temperature increased from 20 °C to 200 °C.

FIGURE 19.  Comparison of R² values on descending section.

FIGURE 20.  (a) R² values for the Malvar model fitting the descending section; (b) R² values for the MBPE model fitting the descending section; (c) R² values for the Continuous Curve model fitting the descending section.

FIGURE 21.  Comparison of curves of each model fitting descending section. (a) HN200; (b) HF200.